Data conversion between color coordinate systems

Abstract

Conversion of color data values from a rectangular coordinate system such as CIELab to a cylindrical coordinate system such as CIELCh using two one-dimensional look-up tables, one each for the C value and the h value. The one-dimensional look-up tables are accessed by defining a new variable γ as the absolute value of the ratio of b and a.

1. Method of converting a color data value (a, b) from rectangular color coordinates to a corresponding color data value (C, h) in polar coordinates comprising:
 calculating a ratio γ based on the absolute value of the ratio of b and a; 
 accessing a first one-dimensional look-up table implementing the values (√{square root over (1+γ 2 )}) on the range of [0 to 1] to obtain a first look-up value; 
 resolving the diagonal quadrant for C based on the ratio γ; 
 calculating C based on the resolved diagonal quadrant and the first look-up value; 
 accessing a second one-dimensional look-up table implementing the values arctan (γ) on the range [0 to 1] to obtain a second look-up value; 
 resolving the octant for h based on the values of a and b and based on the ratio γ of a and b; and 
 calculating h based on the resolved octant and the second look-up value. 
 
   
   
     2. The method according to  claim 1 , wherein the ratio γ of a and b is calculated consistently regardless of the relative values of a and b. 
   
   
     3. The method according to  claim 2 , wherein said steps of accessing the first and second one-dimensional look-up tables include the step of accessing the look-up tables based on the value of γ or based on the value of 1/γ in dependence on the value of γ. 
   
   
     4. The method according to  claim 1 , wherein said step of calculating the ratio of γ comprises the step of calculating γ=a/b or γ=b/a in dependence on the relative values of b and a. 
   
   
     5. The method according to  claim 4 , wherein said steps of accessing the first and second one-dimensional look-up tables comprises the step of accessing the tables based on γ without regard to the relative values of a and b. 
   
   
     6. The method according to  claim 5 , wherein said step of resolving the diagonal quadrant comprises the step of comparing values of a and b. 
   
   
     7. The method according to  claim 5 , wherein said step of resolving the octant comprises the step of comparing the values of a and b and comparing the values of a and b and γ. 
   
   
     8. The method according to  claim 1 , further comprising the step of interpolating values obtained from said steps of calculating C and calculating h. 
   
   
     9. An apparatus for converting a color data value (a, b) from rectangular coordinates to a corresponding color data value (C, h) in polar coordinates, comprising:
 a program memory for storing process steps executable to perform a method according to any of  claims 1  to  8 ; and 
 a processor for executing the process steps stored in said program memory. 
 
   
   
     10. Computer-executable process steps stored on a computer readable medium, said computer-executable process steps for converting a color data value (a, b) from rectangular coordinates to a corresponding color data value (C, h) in polar coordinates, said computer-executable process steps comprising process steps executable to perform a method according to any of  claims 1  to  8 . 
   
   
     11. A computer-readable medium which stores computer-executable process steps, the computer-executable process steps for converting a color data value (a, b) from rectangular coordinates to a corresponding color data value (C, h) in polar coordinates, said computer-executable process steps comprising process steps executable to perform a method according to any of  claims 1  to  8 .